Vol. 58, No. 1, 1975

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A Goldie theorem for differentiably prime rings

John Robert Fisher

Vol. 58 (1975), No. 1, 71–77

The main goal of this paper is to prove analogues of the Goldie theorems for associative rings with derivations. It is shown that a differentiably prime ring, with suitable chain conditions, has a differentiably simple Artinian total ring of quotients, and, conversely, that a differential subring which is an order in a differentiably simple Artinian ring is a differentiably prime ring which has the chain conditions referred to above. A similar theorem concerning differentiably semiprime rings which are orders in differentiably semi-simple rings is also given.

Mathematical Subject Classification
Primary: 16A72
Received: 3 December 1973
Revised: 5 July 1974
Published: 1 May 1975
John Robert Fisher